Constant speed for wheel of any radius when setting speed in radians per second?

Question

In box2d physics engine I can set a motor speed for a joint on my wheel in Radians/Second.

What would be an expression I could set the speed to so the final actual "speed" of the wheel would be the same regardless of wheel radius.

Presently, I'm setting the Wheel speed as a constant, wheelSpeed = 20. But this has the effect of making large wheels faster than small ones. I want the radius to be used in figuring the radians/sec for the motor speed so I will get the same effective speed regardless.

So, if it was a small wheel, it would have to turn much more often than a large one.

I think I need to do something like 2 * PI * Radius / 180 * Speed? Or something similar, but I can't figure it out exactly.

I want to based the wheel motor speed (in radians/sec) it so the final "speed" of the wheels is constant regardless of size of the wheel.

Answer 1

The circumference of the wheel is proportional to the radius, therefore in order to keep the radial velocity in linear units/second constant, divide by the increase in radius.

For example, at radius R, the radial velocity is 1 rad/sec. Then if you increase the radius to 2R, the radial velocity should be 1/2 rad/sec.

Answer 2

There are 2 PI radians in a full circle and your circle length is the circumference (2 PI R).

So, if you want a constant speed of the circumference running past a point, you need a radial speed of:

Y = 2 PI / 2 PI R

or:

Y = 1/R

In other words, make the value a factor of the inverse of your radius.

Answer 3

If v is speed, w is frequency, and r is radius: the equation is v = w * r, or w = v / r. So just take your desired velocity, divide by the radius of the wheel, and set that as the angular velocity.